Best Known (53, 53+20, s)-Nets in Base 2
(53, 53+20, 75)-Net over F2 — Constructive and digital
Digital (53, 73, 75)-net over F2, using
- 21 times duplication [i] based on digital (52, 72, 75)-net over F2, using
- trace code for nets [i] based on digital (4, 24, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- trace code for nets [i] based on digital (4, 24, 25)-net over F8, using
(53, 53+20, 103)-Net over F2 — Digital
Digital (53, 73, 103)-net over F2, using
(53, 53+20, 699)-Net in Base 2 — Upper bound on s
There is no (53, 73, 700)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 9538 207858 908305 016401 > 273 [i]